is known that Founier series of tw) - lalio 1.2 cos(2n-1) (2n-1) on interval 1-1, 1)....
It is known that Fourier series of f(x)=Ixlis 2 cos(2n-1)x (2n-1)2 on interval [ - TT, TT). Use this to find the value of the infinite sum 1 + 1 25 49 1 1 + + +
T 4 Σ cos(2n-1)x 2 (2n-1) 1 on interval [, II, ]. Use this to find the value of the infinite sum 1+. 9 25 1 + + 1 49 + I....
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
2) Given that 4 cos[(2n + 1)x] |x| = = = - - nao ,- < x <te. (2n + 1)2 Find the Fourier series of g(x) = -1 1 -1 < x < 0 0 < x <TE 1
1 3. (12,4) Let b. and consider the series (+1)*** (2n)! Answer the following: na (2n)! A. What does be equal? What does b, equal? Simplify your answers. B. Find the partial sums s, and s, of the series. 4. (14, 5) Find the interval of convergence and the radius of convergence for (x - 2)" 3n-1
Find the interval of convergence of the power series: 5) 00 2n -(4x – 8)" n n=1 E (n + 1)(x - 2)" (2n + 1)! n=0 7) 00 w n(x + 10)" (2n)! n=0
What 2n 7. Determine the radius and interval of convergence of the power series function has this power series as its Taylor series at 07 (10) 27-1 8. Consider the rational function (x) Find the Taylor series at 0 of (2) and determine its radius and interval of convergence. (10) 2-1
5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1 500). Its spectrum X1c" consists of a pair of spectral lines at positive and negative frequencies. Use the MATLAB command fft to find and plot the signal's spectrum using various values of N.
4. a) Find the interval of convergence. 7m b) Determine whether the series in a) converges or diverges at the endpoints of the interval 5. Find the Maclauren series for f(x) = cos(2x). Include an expression for the neh term in the series.
4. a) Find the interval of convergence. 7m b) Determine whether the series in a) converges or diverges at the endpoints of the interval 5. Find the Maclauren series for f(x) = cos(2x). Include an expression for...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...